【4月19日】数学学术讲座

报告题目：Image segmentation using Bayesian inference for convex variant Mumford-Shah variational model

主讲人：文有为教授（湖南师范大学）

时间：2023年4月19日（周三）15:30 p.m.

地点：北院卓远楼305会议室

主办单位：统计与数学学院

摘要：

The Mumford-Shah model is a classical segmentation model, but its objective function is non-convex. The smoothing and thresholding (SaT) approach is a convex variant of the Mumford-Shah model, which seeks a smoothed approximation solution of the Mumford-Shah model. The idea of SaT is to separate the segmentation into two stages: a convex energy function is first minimized to obtain a smoothed image and then a thresholding technique is applied to segment the smoothed image. The energy function consists of three weighted terms and the weights are called the regularization parameters. It is important to select the appropriate regularization parameters to obtain a good segmentation result. Traditionally, the regularization parameters are usually chosen by trial-and-error, which is a very time-consuming procedure and is not practical in real applications.

In this talk, we apply Bayesian inference approach to infer the regularization parameters and estimate the smoothed image. We analyze the convex variant Mumford-Shah variational model from the statistical perspective and then construct a hierarchical Bayesian model. Mean field variational family is used to approximate the posterior distribution. The variational density of the smoothed image is assumed to have Gaussian density, and the hyperparameters are assumed to have the Gamma variational densities. All the parameters in the Gaussian density and Gamma densities are iteratively updated, hence the proposed method is parameter-free.

Experimental results show that the proposed approach can obtain good segmentation results. Although the proposed approach contains an inference step to estimate the regularization parameters, it requires less CPU running times to obtain the smoothed image comparing to previous methods.

主讲人简介：

文有为，湖南师范大学数学与统计学院教授，博导，湖南省计算数学与应用软件学会副理事长。获香港大学博士学位，曾在新加坡国立大学、香港中文大学从事访问研究员、博士后等工作。主要研究方向为科学计算、数字图像处理与计算机视觉，在SIAM J. Sci. Comput., SIAM J. Imaging Sciences, Multiscale Model. Simul., SIAM J. Matrix Anal., IEEE Trans. Image Process.等期刊发表论文30余篇，主持国家自然科学基金4项。以第一完成人身份，获2019年湖南省自然科学奖二等奖。